承る and 注文: the provider politely receiving an order
Distinguish the customer's order action from the provider's 承る. Availability of a telephone channel or a planned visit to hear requests does not establish that a request has been received.
The provider receiving an order
承る, read うけたまわる, politely expresses hearing or receiving. 当店では、ご注文を電話でも承ることができます。 says that the shop can also accept orders by telephone.
The shop is the receiving party. ことができます announces an available channel; it does not report that a particular customer's order has already been accepted.
The customer making an order
注文, read ちゅうもん, means order. 食堂で温かいうどんを注文した。 says that someone ordered warm udon at the cafeteria.
This is the customer's completed order action. Keep it distinct from the provider politely receiving the order instead of assigning both roles to the same actor.
A visit planned to hear requests
ご希望の詳細を承るため、担当者が席まで参ります。 says that a staff member will come to the seat to hear the requests in detail.
承るため gives the visit's purpose, while 参ります announces the planned visit here. A plan to hear the details does not report that all details have already been heard.
Does 電話でも承ることができます。 state that a particular customer's order has already been taken?
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No. It announces that orders can also be accepted by telephone. Whether a particular order has already been taken requires separate information.